A mapping (also called match) between entitiesIn this work we accept any input ontology in the OWL 2 language [1]}. We refer to (OWL 2) concepts, properties and individuals as entities. of two ontologies \(\mathcal {O} _1\) 
and \(\mathcal {O} _2\) 
is typically represented as a
4-tuple \(\langle e_1,e_2,r,c\rangle \)  where \(e_1\)  and \(e_2\)  are entities of \(\mathcal {O} _1\)  and \(\mathcal {O} _2\) ,
respectively; \(r\)  is a semantic relation, typically one of \( \lbrace \sqsubseteq , \sqsupseteq , \equiv \rbrace  \) ; and \(c\)  is a confidence value,
usually, a real number within the interval \(\left(0,1\right]\) . For simplicity, we refer to a mapping
as a pair \(\langle e_1,e_2 \rangle \) .
An ontology alignment is a
set of mappings \(\mathcal {M}\)  between two ontologies \(\mathcal {O} _1\)  and \(\mathcal {O} _2\) .
